Normal Distribution Calculator
Probabilities under the bell curve.
Enter your values
ⓘ Live results
Results
- P(X < x)
- 0.908789
- P(X > x)
- 0.091211
- Z score
- 1.33333
- Percentile
- 90.88%
- P(x < X < x₂)
- 0.068461
Quick answer
The normal distribution converts any value to a z-score, then reads the area under the standard bell curve.
z = (x − μ) / σ
How to use the Normal Distribution Calculator
- 1Enter the population mean and standard deviation.
- 2Enter the value you are testing.
- 3Add a second value for a range probability.
Worked example
Using the values the calculator loads with:
Inputs
- Mean μ100
- Standard deviation σ15
- Value x120
- Second value (optional)130
Results
- P(X < x)0.908789
- P(X > x)0.091211
- Z score1.33333
- Percentile90.88%
- P(x < X < x₂)0.068461
Frequently asked questions
What is the 68-95-99.7 rule?
About 68% of data lies within 1 SD, 95% within 2 and 99.7% within 3.
Is my data normal?
Check a histogram or QQ plot; heavily skewed data needs different tools.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.